I would recommend against using the Servo alpha against Tor, though; some web security features (eg stuff like CORS, though our CORS support is okay) aren't there yet IIRC.
(Of course, this will change over time, just that I don't expect it to be 100% secure by June)
Rust is secondary to the issue. I am more concerned about how much browsers divulge when asked. Test your browser at https://www.browserleaks.com/